Experimental setup–
The system under consideration is illustrated schematically in Fig. REF . A triangular array of spatially-separated optical beams (channels), labeled Ch1, Ch2 and Ch0, propagate in a warm atomic vapor cell. Each channel undergoes a \(\Lambda \) -type EIT interaction with the same configuration (Fig. REF (b1)), where a relatively strong control and a weak probe fields conspire to create a collective spin wave \(\rho _{12}\)  (ground-state coherence) in the atomic ensemble. We apply co-propagating probe and control beams, such that the EIT linewidth is not Doppler-broadened.
While EIT creates a linear mapping between the probe light and the spin excitation [1]}, [2]}, spin waves in different channels couple to one another with a rate \(\Gamma _c\)  via random atomic motion and wall bouncing [3]}, [4]}. Although the random atomic motion renders the coupling dissipative, optical phases imprinted upon the atomic spin states are preserved throughout the dynamics, and constitute a convenient control over the light transport.
To study light transport, we take Ch1 and Ch2 as the two optical nodes, and regard Ch0 as part of the reservoir, together with the surrounding atomic ensemble. Since Ch1 and Ch2 couple to the same reservoir, we can manipulate the coherence in the reservoir through Ch0, and thus control the dissipative inter-channel couplings.
